Saddlepoint Approximation Reliability Method for Quadratic Functions in Normal Variables


If the state of a component can be predicted by a limit-state function, the First and Second Order Reliability Methods are commonly used to calculate the reliability of the component. The latter method is more accurate because it approximates the limit-state function with a quadratic form in standard normal variables. To further improve the accuracy, this study develops a saddlepoint approximation reliability method that does not require additional transformations and approximations on the quadratic function. Analytical equations are derived for the cumulant generating function (CGF) of the limit-state function in standard normal variables, and then the saddlepoint is found by equating the derivative of the CGF to the limit state. Thereafter a closed form solution to the reliability is available. The method can also apply to general nonlinear limit-state functions after they are approximated by a second order Taylor expansion. Examples show the better accuracy than the traditional second order reliability methods.


Mechanical and Aerospace Engineering


This material is based in part upon the work supported by the National Science Foundation under Grant Number CMMI 1562593.

Keywords and Phrases

Number theory, Analytical equations; Closed form solutions; Cumulant generating functions; Limit state functions; Reliability methods; Saddle-point approximation; Second-order reliability methods; Second-order Taylor expansion, Reliability

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Article - Journal

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